1. Field of the Invention
The present invention relates to a parameter extraction method of an element having a plurality of parameters, a method for inspecting a circuit operation using an element parameter extracted by the parameter extraction method, and a storage medium having a program to perform the parameter extraction method. In particular, the present invention relates to an element parameter extraction method, a method for inspecting a circuit operation, and a storage medium having a program to perform the parameter extraction method, in semiconductor circuit simulation for inspecting an operation of a designed circuit based on a given parameter that expresses an operation of a circuit component element using a model formula of a semiconductor element in designing a semiconductor circuit.
2. Description of the Related Art
In circuit simulation (also referred to as circuit operation inspection), generally, a circuit operation is inspected by inputting several conditions required for circuit simulation, such as circuit connection information, an element parameter, an analysis condition, and an output condition, and by using the inputted information with or without modification.
Among the inputted information, the element parameter is a parameter included in a model formula that mathematically expresses a relation of physical quantities corresponding to an input and an output of an element. For example, BSIM3 MOSFET Model or the like is given as the model.
Instead of using the element parameter, circuit simulation can be conducted by using a method of reproducing an operation of an element in a device simulation apparatus. However, when a device simulation apparatus is used in combination with a circuit simulation apparatus, analysis scale expands despite improvement of analysis accuracy, and moreover, analysis speed gets slower, which is impracticable. Thus, a device simulation apparatus is not often employed.
Therefore, in a case of simulation of a large-scale circuit, generally, an operation of an element that forms a circuit is expressed by a model formula and its element parameter, and the information on the model formula and the element parameter is processed in a circuit simulation apparatus. Thus, circuit simulation is conducted. In this case, if element characteristics reproduced from the model formula and the element parameter do not match well with characteristics of an element that actually forms a circuit, a result of the circuit simulation does not match with an analysis result of the circuit that is actually formed.
Therefore, there are some evaluation formulae for quantitatively evaluating the match between actual element characteristics and characteristics expressed by the model formula. When it is assumed that an input/output response obtained from physical measurement of an actually formed element be an actual measurement value (hereinafter also referred to as meas) and an input/output response calculated from the given model formula and its element parameter be a calculation value (hereinafter also referred to as sim), a difference between each actual measurement value and each calculation value can be evaluated. In other words, the difference between each actual measurement value and each calculation value can be regarded as a difference between output values of the actual measurement value and the calculation value of which input values are equal to each other.
Instead of the difference between each actual measurement value and each calculation value, a difference between the whole actual measurement value and the whole calculation value can be evaluated. In general, the difference between the actual measurement value and the calculation value is evaluated by a mean error or a mean square error of the difference between the actual measurement value and the calculation value (see, for example, Reference 1: Japanese Published Patent Application No. H8-29255 and Reference 2: Japanese Published Patent Application No. 2001-35930). Each actual measurement value is given a number, and the calculation value of which input value is equal to the i-th actual measurement value is similarly numbered as the i-th calculation value. Then, when the difference between their output values is denoted as error (i), the mean error can be evaluated by (Formula 1).
                              100          N                ⁢                  (                                    ∑                              i                =                1                            N                        ⁢                          error              ⁢                                                          ⁢                              (                i                )                                              )                                    [                  Formula          ⁢                                          ⁢          1                ]            
Moreover, the mean square error can be evaluated by (Formula 2).
                              100          N                ⁢                                            ∑                              i                =                1                                                                                              ⁢                N                                      ⁢                                          {                                  error                  ⁢                                                                          ⁢                                      (                    i                    )                                                  }                            2                                                          [                  Formula          ⁢                                          ⁢          2                ]            
It is to be noted that, in (Formula 1) and (Formula 2), N is the number of actual measurement data, which is also equal to the number of the calculation data.
As thus described, there are formulae that evaluate the match between each actual measurement value and each calculation value of element characteristics and that evaluate the match as a whole between the calculation value and the actual measurement value of element characteristics. However, when using these formulae, in some cases, the degree of the match as a whole between the actual measurement value and the calculation value based on the appearance did not correspond to the degree of the match obtained by quantitatively evaluating with the above (Formula 1) and (Formula 2).
Hereinafter, as a specific example, description is made of the estimate on the difference between the actual measurement value and the calculation value (hereinafter referred to as an error regardless of whether it is the difference of each data or the difference as a whole), by using drawings and flow charts.
FIG. 9 is a flow chart of a conventional method for evaluating errors. First, a formula for evaluating an error, which is a difference between an actual measurement value and a calculation value, is selected (Step S901).
Next, an error at each data point is stored (Step S902). Here, the term “store” means temporal storage for calculating a mean error or a mean square error in the next step.
Subsequently, the mean error and the mean square error are calculated by using the error stored at each data point (Step S903).
The mean error and the mean square error calculated in Step S903 are outputted to complete the evaluation on the error, which is the difference between the actual measurement value and the calculation value (Step S904).
FIG. 10 shows an actual measurement value and a calculation value concerning gate voltage−drain current characteristics of a TFT (Thin Film Transistor, hereinafter also referred to as TFT). In FIG. 10, the actual measurement value is shown by a curved line expressed by circular plots, a calculation value 1 is shown by a curved line expressed by x-marks, and a calculation value 2 is shown by a curved line expressed by triangular marks. As for FIG. 10, assuming that the error between the actual measurement value and the calculation value be obtained by dividing the difference between the actual measurement value and the calculation value by the actual measurement value, Table 1 shows the mean error of (Formula 1) and the mean square error of (Formula 2).
TABLE 1mean squaremean errorerrorerror by difference between425443.1236499.4actual measurement value andcalculation value 1error by difference between38.059396.779373actual measurement value andcalculation value 2
In FIG. 10, it seems that the calculation values 1 and 2 are both similarly apart from the actual measurement value. However, when the error between the actual measurement value and the calculation value is evaluated by the mean error of (Formula 1) or the mean square error of (Formula 2), the difference between the both reaches several tens of thousands times. It is to be noted that (Formula 1) and (Formula 2) are the comprehensive and quantitative evaluation formulae for the actual measurement value and the calculation value.
The widening of gap in the mean error and the mean square error is caused by dividing the difference between the actual measurement value and the calculation value by the actual measurement value. By dividing the difference between the actual measurement value and the calculation value by the actual measurement value, evaluation can be made by the proportion (%) of the difference between the actual measurement value and the calculation value, which enables the evaluation to be more accurate. However, the smaller the actual measurement value is, the more the difference between the actual measurement value and the calculation value is amplified. Accordingly, if the difference is the same, the smaller the actual measurement value is, the more a result of dividing the difference between the actual measurement value and the calculation value by the actual measurement value is increased. That is to say, among the whole actual measurement values, a relatively smaller value contributes more to the mean error or the mean square error. In particular, when the actual measurement value changes exponentially, the relatively smaller actual measurement value contributes more significantly to the mean error or the mean square error.
For example, in vicinity of threshold voltage of a transistor, as shown in FIG. 11, the calculation value is several tens of thousands times the actual measurement value, so that the difference between the actual measurement value and the calculation value was regarded as a significant difference. FIG. 11 shows gate voltage−drain current characteristics of a TFT, in which the actual measurement value and the calculation values are shown with logarithm on a vertical axis. FIG. 11 is substantially the same as FIG. 10.
However, in order to extract the element parameter, it was necessary that after making the actual measurement value and the calculation value match with each other as well as possible, the element parameter inversely obtained from the calculation value be extracted. If not, even the accuracy of circuit simulation could not be expected. Thus, it was necessary to confirm the match between the actual measurement value and the calculation value on the graph or confirm the match by the aforementioned mean error or mean square error (MSE).
Therefore, it is a problem that, in evaluation on the degree of the match between an actual measurement value and a calculation value based on the appearance and the error between an actual measurement value and a calculation value based on the mean error or the mean square error, there is a gap in the degree of the match between the obtained actual measurement value and calculation value.